What is the difference between positive and negative rotation?
The Euler rotation is calculated by a rotation matrix which uses sine and cosine; These functions are periodical, which means it wouldn't make any difference whether you set the value for &Phi; to &Phi;+360° or &Phi;-360°.


image by Udo Brechtel (Wikipedia); the label Einheitskreis means unit circle 

Rotating a cube by 90 degrees (or a rectangle by 180°) wouldn't have any effect to the un-textured appearance of the mesh, but it would for materials (think of it like differently textured faces). 

As @cegaton already commented, animations rely on the direction of your rotation. An arm could reach the same position by rotating 90° in one or 270° in the opposite direction.

When you increase the rotation by e.g. 720° between two keyframes the object would rotate twice around the keyframed axis. Note that Quaternions behave differently you can't express rotations > 360° with them.